A sports arbitration panel set aside objections from the International Olympic Committee.
The IOC had banned Prusis, overruling the International Bobsled Federation.
Prusis appealed to the Court of Arbitration for Sport, a panel designed to keep eligibility disputes out of the law courts.
"The decision sends a strong and unambiguous message to the IOC"
Attorney Erik A. Christiansen
The panel ruled the IOC must prove a sports federation had violated the Olympic charter.
Otherwise, it could not take an action that would compromise the independence of the sports federation.
It reaffirmed that sports federations "can decide how to deal with doping offences which come within their jurisdiction."
Prusis, pilot of the two-man and four-man Latvian sleds, tested positive for the steroid nandralone after a November training run at the Olympic track in Park City, Utah.
The bobsled federation then banned him on 7 January from World Cup competition and the Olympics.
But Prusis and Latvian Olympic officials appealed, blaming the positive test on dietary supplements.
The bobsled federation agreed and imposed a three-month retrospective suspension on Prusis that was to end on 9 February, making him eligible for the Winter Games.
The IOC, however, said the timing of a three-month ban had been "carved out" to allow Prusis to compete against the spirit of anti-doping efforts.
Attorney Erik A. Christiansen, who represented Prusis, said the decision sent "a strong and unambiguous message" to the IOC.
"It cannot arbitrarily, and without any prior notice, penalise an Olympic athlete who already has been penalised by the athlete's international federation and served their penalty."
This was the first drug case before the IOC in Salt Lake City.
The Olympics start on 8 February, with the bobsleigh competition beginning on 16 February.